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Paper IPM / P / 7604  


Abstract:  
Introducing the associated Laguerre functions in terms of two nonnegative integers, we obtain simultaneously and separately realization of the laddering equations with respect to each of the integers by means of two pairs of ladder operators. Besides, two different types of shapeinvariance symmetries are realized. This approach leads to a derivation of shapeinvariance equations of third type which are realized by two simultaneous raising and lowering operators of two parameters.
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